5.1.3 Thermal properties of materials

Specific heat capacity
The specific heat capacity of a substance is defined as the energy required per unit mass to change the temperature by 1K/1°C. It has the unit J/(kg K). The specific heat capacity 'c' can be calculated using the following equation...

E = mcΔθ

E is the energy supplied (in J)
m is the mass of the substance (in kg)
Δθ is the change in temperature (in K or °C)

For example, water has a specific heat capacity of 4200 J/(kg K) meaning 4200J are required to increase the temperature of 1kg of water by 1K.

We need to be able to determine the specific heat capacity experimentally... we can do this by using an electrical heater. You should carefully insulate the substance to minimise energy loss to the surroundings and the liquid must be carefully stirred to ensure is has uniform temperature. Use a circuit with an ammeter, voltmeter (across the heater) and a variable resistor. Determine E using E = ItV (where t is the time taken to change the temperature of the substance by Δθ). This means that c can be calculated using the following equation...

c = (ItV)/(mΔθ) 

Plot a graph of temperature against time. Rearrange the above equation to give...

E/Δt = mc (Δθ/Δt)

Δθ/Δt is the gradient
E/Δt is the constant power supplied (power is work/time)
 c = P/(m x gradient).

This might be a bit confusing so may be a good idea to look over this again (and again... and again... and again...)

Methods of mixtures
This is another way in which we can determine the specific heat capacity of a substance. Known masses of two substances a different temperatures are mixed together and their final temperature (their temperature at thermal equilibrium) is recorded. This allows for the specific heat capacity of one to be calculated provided the other is known. For example...

A block of mass 0.1kg is heated to 100°C and then placed in 0.2kg of liquid which is at 20°C. The liquid and the block reach thermal equilibrium at 26°C. Determine the specific heat capacity of the metal. The specific heat capacity fo the liquid is 4200 J / (kg K).

Okay so thermal energy is transferred from the block to the liquid meaning that energy transferred from block = energy transferred to liquid...

m(block) x c(block) x Δθ(block) = E + m(liquid) x c(liquid) x Δθ(liquid)

0.2 x c(block) x (100-26) = 0.2 x 4200 x 6

7.4 c(block) = 5040

c(block) = 5040 / 7.4 = 681 J / (kg K)

Constant-volume-flow heating
If i'm, honest, i'm not sure if we need to know this (can't really find it in the spec) but we studied it in class so here it is if you want it...

Constant-volume-flow heating is a technique used to heat a fluid passing over a heated filament (e.g it is used in many showers/dishwashers etc). Liquids are virtually incompressible meaning a given volume of a liquid in a pipe is equivalent to a given mass so the rate of flow can be regarded as the mass flowing through the pipe and passing over the heating element per unit time in kg/s. For constant-volume-flow heating E = mcΔθ becomes...

E/Δt = (m/Δt)cΔθ

NOTE: do not get this mixed up with E/Δt = mc (Δθ/Δt) from the experiment!!! they are different arrangements.


Specific latent heat
Okay so this is the energy needed to change the phase per unit mass while at a constant temperature. There are two types...

• Specific latent heat of fusion (solid to liquid/liquid to solid)
• Specific latent heat of vaporisation (liquid to gas/gas to solid)

They are both calculated using the equation...

L = E / m

As we know from 5.1.2 the energy transferred to a substance at its melting point increases the internal energy of the substance by increasing the electrostatic potential forces between the atoms/molecules without increasing its temperature. We need to know how we might go about determining the specific latent heat of fusion and vaporisation of a substance...

The specific latent heat of fusion:

• Create a circuit with an ammeter, switch, variable resistor, and voltmeter across a heater.
• Introduce the heater into a funnel of ice (with a beaker underneath to collect the melted ice/water)
• Use a thermometer to ensure the ice is at melting point (the ice should be seen to be just starting to melt when the heater is switched on).
• Measure the potential difference across the heater, the current in the heater, and the time during which the heater is used to determine the energy transferred to the ice by the equation E = ItV
• Measure the mass of water (the mass if the substance, ice, that changes phase from solid to liquid)
• The specific latent heat of fusion can be determined using L = (ItV)/m

The specific latent heat of vapourisation:

• Use an electrical heater with a condenser to collect and measure the mass of liquid that changes phase.
• The Lv can be found using the same equation, L = (ItV)/m

Energy conversions
I just wanted to do a tiny bit on energy conversions to help with which equations to use when depending on what questions get asked...

• heating a solid to melting point, E = m x c(solid) x Δθ
• melting a solid at constant temperature, E = mLf
• heating the liquid to boiling point, E = m x c(liquid) x Δθ
• boiling the liquid at constant temperature, E = mLv